Omneya al-Naggar, an Egyptian schoolteacher based in Alexandria, and Orly Noy, an Israeli journalist of Iranian origin living in Jerusalem, are both working mothers.
"You ask if we can reconcile our worlds," begins Orly.
"I want to believe that we can, but I think that it would have to start on a cultural level rather than the political one."
Orly and Omneya begin to discuss the language of the conflict, disputing the use of the term 'legitimacy' to describe the Palestinian case.
"You know that in Israel there is a substantial number of people who believe that the Jews are the only legitimate owners of the Holy Land, because it says so in the bible," wrote Orly.
"I feel that the discussion about legitimacy is too close to the one about what's 'right' and 'wrong'. That's why I prefer the term 'narrative', because this is your story and nobody can tell you if it's a legitimate one or not.
"The fact that you didn't answer my question is telling since I didn't project any judgement about right and wrong," replied Omneya.
"And since when was politics about right or wrong? Politics is all about interests."
Omneya described visiting former concentration camps in Eastern Europe, and Orly asked if the experience changed her views on the Arab-Israeli conflict.
"What Auschwitz means to me is a failure of European democracy and humanism at a certain stage of its historical development," Omneya writes.
"In terms of world history, I think it has a good lesson. Genocide is an evil machine, so there is no point of repeating the same history in Israel."
The feature was in the top 10 of most visited pages on both BBC.co.uk and BBCArabic.com when it was first published.
"We were trying to find ways of generating debate around views exchanged by people from different perspectives," said Hosam El Sokkari, editor of BBCArabic.com.
"It was exciting to see this remarkable and genuine interaction in such a civilised and well-informed manner."
Mr El Sokkari told dotJournalism that offering a platform for this kind of interaction is an important element of the BBC Arabic service.
"Omneya and Orly is not a first for us and will not be the last exciting project that aims at offering our users a platform to exchange their views," he said.
BBC viewers around the world have joined the debate by posting their comments to the site.
Samer of London wrote that he believes the majority of Arabs and Israelis want peace.
"I feel, as an Arab, that we are divided by misconceptions and by media coverage of the extreme. Initiatives like this one by the BBC definitely help bridge the gap."
• Last week BBC Arabic launched a campaign to encourage its radio and online audience to interact with the site in response to coverage of news and current affairs.
"Together with the Have Your Say section on bbcarabic.com these interactive programmes have turned BBC Arabic into a hub across the Arab-speaking world for free and open debate as people call, email and message us," said Hosam El Sokkari, editor of bbcarabic.com.
See also:
http://news.bbc.co.uk/1/hi/world/middle_east/3561133.stm
http://news.bbc.co.uk/hi/arabic/talking_point/newsid_3558000/3558227.stm
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